Bach wrote fifteen inventions for two voices and fifteen inventions for three voices. He wrote them for his pupils, and for over a century all serious piano students have practiced these simple polyphonic compositions as a preparation for studying the more complicated masterworks. We are going to learn the Two-Part Invention in F Major (Number 8).

Learn This Invention Slowly

The invention is in three sections. The first section starts out as a canon at the octave and modulates to the key of C. The second section begins in similar fashion in the key of C, modulates to G minor and other keys and leads into the third section, which begins in Bb major and ends in F major. This third section is a transposed repetition of part of the first section.

Listen to It

The entire invention is built on three main figures. The first is constructed on the F major chord—F F F ; the accents fall on the upper note in each pair. Play this in each hand, and listen to it carefully. Spread the hand so that the fingers reach all the notes in one grasp. The right hand begins on the F above middle C, and the left hand begins on the F below middle C.

Make it a Part of Yourself

The second figure begins with the last note of the previous figure. It is a sequence of four descending notes repeated three times; each group of four begins on the note above the last of the previous four. All except the first of the notes in this sequence move twice as fast as the first figure.

Thus

The accents fall on the last of each group of four.

Play this in each hand. Use the same first four fingers for the four note group each time it comes, unless very inconvenient; thus your fingers help you to remember the form of the melodic line.

You Will Do Well If You Have Come This Far at the End of the First Week

Put the first and second figures together now. Play the two of them in each hand many times, until your ear and fingers are very familiar with them—until they are very familiar with them.      

A

	F
Now invert the first F major chord so that it becomes	C	and play the first
	A
figure on this chord. You will notice that the third of the chord, A, feels much weaker than the good solid root, F, in the original figure. Bach noticed this
too, so he changed the figure to sound The C is much more
satisfactory than the A would be there, isn’t it?

Join these three measures together and play them many times in each hand. For convenience in continuing, use i 2 in the right hand and 5 3 in
                                                                                                     C                 C
the left hand for the last two notes of this passage. The last A is the first A of the next figure.

The third figure is very simple—A ®b — and moves in the faster speed. Throughout this entire invention there are just the two types of notes, one twice as fast as the other. This figure plays itself three times up there on A, then drops a third lower and plays itself three times on F, then drops a third lower and plays itself three times on D, and then drops a third lower to end on B. The easiest fingering for this figure is 2 4 3 4 in the right hand and 3 1 2 1 in the left hand; but each time you move from one position to another, you had better use a convenient finger to reach out and grasp the first note of that new position easily. Practice thus far in each hand.

Third Week

Continuing in the right hand, play the V7 chord on G. Bach uses this for
the figure, but does not give us the		which we might expect.
In order to give the stronger thrust upward, he plays It does
send you zooming up to G, doesn’t it? The easiest fingering for this is I 3 I 3 I 3.

The second figure now returns. Beginning with the 3rd finger where it ended on G, continue with the regular finger pattern 4 3 2 1, 4 3 2 1, 4 3 2 1
—that is

Here you pause just one extra pulse and then pick up the same figure again, beginning on D. The pause, however, only leaves room for three
notes in the first groupthus:

This is a good place to stop; the Bt| has brought us into the key of C. Practice this in the right hand only.

Continuing in the left hand, play the C major chord with the G at the bottom. Or better, immediately after the B which ended the previous portion, play
the figure on this inverted C major cord:

Notice that in the inversion Bach again chooses the root as stronger than the G for the next to the last note of this figure.

Instead of progressing on up to the octave G, as the right hand did, land squarely on F at the close of this figure and then progress down in similar fashion to the right hand, but always one note lower:

	reaching this comfortable
	and we had better stop on C, even

though it is not on the accent. G is the next note, in case you are one of those people who just must end on an accent—the upper G. Practice this in the left hand only.

Fourth Week

To bring this first section to a close, the right hand now has a little codetta, beginning with the little finger on C an octave above the close of above the close of the last portion:

Listen to the strong downward progression in the lower notes

here; it seems to suggest the perfect cadence which you practiced in Chapter 4. Practice the entire first section in the right hand. After the final C of the last portion of the left hand, we find the simple little

cadence and no – satisfying final C. Practice the entire first

section in the left hand.

Now comes the fun! Put the two hands together. The right hand begins first; the left hand begins when the right hand plays the E in the second figure. Of course, the second figure goes twice as fast as the first figure, so the right hand is here playing two notes to each one in the left. The process is then reversed and the right hand plays the first figure, while the left hand plays the second figure, two notes to one in the right hand. Again the process reverses as the right hand begins the third figure. Following this, the two hands come together for a time in the third figure. You will now feel the way the hands fit together and can continue to the end.

This sounds complicated. Actually it is much more com­plicated than it sounds—if you have never before played polyphony. Do not be startled when the left hand makes a terrible discord at its first entrance; that is the way it should sound, but you never heard polyphony this keenly before. Keep going. Do not be surprised when your two thumbs land on the same F at the end of the first figure in the left hand; they should. After you have conquered the three figures hands together, you will find it becomes astonishingly easy. In this short time you have conquered polyphony; you will never be the same again!

Fifth Week

You are able to play this first section with each hand separately very well, but you find that you keep forgetting it as you put them together. Go back and relearn the single hand and then try again together. It may take several hundred attempts; you are forcing yourself to hear two separate melodic lines at once. You have never done this before. Your appreciation of music will expand enormously in the process!

Without waiting to perfect the first section hands together, continue to prepare the next section hands separately.

The left hand leads off in the second section by playing exactly the same part with which the right hand opened the first section, except that it is now in the key of C. Begin an octave below middle C and play the first figure and then the second figure and then the first figure inverted. This would end on E, if it followed the original right hand exactly; but at this point the left hand takes a fill-in figure Eb p#, repeated slowly three times, and then resolves to the thumb on G. Notice the suggestion of the diminished seventh chord here and its resolution to the tone just above the lower note. This VII7 brings us into the key of G minor.

Continue the left hand by playing the second figure downward in minor—melodic minor—from the G: G F Eb D Eb D C Bb C Bb A G. Use the 1234 fingering, even though it requires you to put your thumb on the black key; the regularity of fingering is easier and helps you to feel the sequence. The left hand now jumps back up an octave and plays the first figure on the G minor chord, beginning with the little finger on G. It continues with the second figure down the scale of G minor again and ends with the 4th finger on G. This is a good stopping place. Practice this much of the second section in the left hand.

The right hand begins the second section in similar fashion, playing the first and second figures on the C above middle C. However, instead of continuing with the inversion of the first chord, it proceeds with a new figuration

At first hearing this sounds complex; but note that the repeated A is merely a           baffle for the melody moving in the lower part:

The ear easily grasps this melodic figure. You will find it easier to use the thumb on C throughout this passage. Practice this much of the second section in the right hand.

Sixth Week

We left the left hand with the fourth finger on G. This continues with the figure we have just described in the right hand, thus:

Notice that here E is the baffle tone and the melody GpGg catches the ear. Immediately this figure is repeated one tone lower:

Learn the left hand thoroughly up to this point.

Meantime the right hand continues with the first figure on the G minor chord. If we begin with the B(?, which was the last note practiced in the previous segment, we have: 
This continues downward with the second figure in the key of G minor and then the first figure is played on the inversion of the G

Then follows the same diminished seventh fill-in figure which the left hand played a while back: minor chord: repeated slowly three times. Next comes the most trouble­some measure in the entire piece; it is six notes on the D minor chord: We had better stop here and learn thus far very well with each hand before trying to put them together. Learn the right hand thoroughly up to this point.

Seventh Week

In putting the two hands together in this second section, the left hand begins first. Bach prepared for this entry by omitting the final C in the first section. The two hands have now changed places, and the right hand enters as the left hand plays the B in the second figure. If you have conquered the first section, you will have little difficulty in continuing with the second. Practice this far hands together.

Before going farther it would be well to practice a sequence of unfamiliar seventh chords which Bach employs in the following passage. The first is the V7 on C; the second is the seventh chord on B, all white keys; the third is the V7 on A; the fourth is the seventh chord on G with a Bb; the fifth is the seventh chord on F, all white keys. Practice this descending sequence of seventh chords in both hands till you can find them easily.

In the right hand the figure in D minor leads right up to this first seventh chord, which is played with this figuration:  Begin with the 3rd finger on G. Do not be misled by the upper Bb, which is used as a baffle, but let the ear follow the lower progression. Also, note the way the figure sticks to the seventh chord. This figure is then repeated on the second seventh chord, using a C# for the passing tone. It is then repeated on the third seventh chord.

On the fourth seventh chord the figure is changed to resemble an inversion of the original figure at the very beginning of the invention:  Notice that this figuration employs no passing tones; all of the notes lie in the chord. It is taken at the speed of the original figure. This same figura­tion is then repeated on the fifth seventh chord except that the final tone is Eb and leads into the third main section.

In the left hand this sequence uses the figuration for the first three seventh chords, which the right hand used on the fourth and fifth, with one change—the final note is the third of the chord instead of the seventh, thus  You will find this simple to do. In place of the fourth chord, however, the left hand reaches down to the low D and, using the G minor chord, plays the following figuration:

Notice that this G minor chord is the lower portion of the seventh chord. Notice also, the similarity of the figuration to that played by the right hand on the first three seventh chords. This right hand figuration would have sounded weak as the bass, so Bach changed it to emphasize the low D but kept it as close as possible to the one he had already used. This figuration is repeated one tone lower on the F major chord with C as the first and lowest tone. This leads into a Bb and the left hand then plays the original first figure on the inversion of the Bb chord, thus:

We are now ready for the third main section in the left hand.

We are now ready for the third main section in the left hand.

Eighth Week

Practice the second section in each hand and then in both hands.

The last measure learned in the left hand will be extra, because it serves as a splice into the third main section. The final Eb in the right hand of the middle section leads into the third figure played on  This is repeated three times and then drops a third to repeat three times on Bb, etc., following exactly the line in the right hand of the first section but now in a different key. Your ear will guide you safely to the end of the piece, where you may play a satisfying F chord, instead of a lone F. The piece began in F and modulated to C during the first section. The third section picks up this figuration in Bb and modulates to F.

The left hand playing the first figure on the inversion of the Bb chord defines this key for us and leads up to play the third figure on D. This fits in familiarly with the right hand and leads easily to the end. This third section is practiced most easily with both hands. Play the entire invention.

If you are familiar with music notation or have been attempting to learn it from the examples given in this book, you may wish to check your playing of this Invention against the notation. For this purpose the entire composition is given in Appendix 11. The reader, however, cannot be too strongly warned against looking at the music, except as a last resort. When the ear player is searching for the next note and has only a shadowy clue as a guide, he is doing his best learning—he is stretching his ear to a greater sensitivity than he has ever experienced before. If he substitutes a wrong note, no great harm is done; someday he will be interested to consider why the composer used a different one. If possible, therefore, learn the entire Invention, and then check it against Appendix II. This entire chapter is not easy; read and re-read it. Follow the directions very carefully.

WHAT TO DO Learning the invention outlined in this chapter will be quite an accomplishment. The Bach Two-Part Invention in C Major (Number i) is the next easiest to learn in this manner. If you wish to try ajugue, the Number 5 in D major from the Well-Tempered Clavichord is the easiest. The prelude to the first fugue in C major in the Well- Tempered Clavichord is very easy to learn and offers some interesting polyphonic progressions if one follows the continuity of the chordal tones and is not misled by the figuration on the successive chords. Try portions of any familiar Bach number. The various arrangements of BacKs Jesu, Joy of Man's Desiring offer some interesting use of polyphony which is not complex.

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